Second Order Analysis And Dynamic Analysis Of High-rise Building Structure

With the height increasing, the lateral rigidity of high building structure was relatively weaker, and the arrangement of plane and elevation became more and more complicated. The second order analysis and the dynamic properties of high-rise building are important contents of research because of the control factors of horizontal load,earthquake action and huge vertical load of itself.Under the assumptions of rigid floor and continuum method, taking the parallel Timoshenko beams as calculation model of the high-rise building structure with multi-lateral resistant elements, assimilating the height of structure to time, the lagrangian of structure was deduced. Further more, by introducing the dual variable of the generalized displacements, the Hamiltonian function and Hamiltonian duality equations were derivated, which led the description of the question from Lagrange system to the Hamilton dual system, this paper founded the state space expression of second order analysis and the dynamic properties of high-rise building structure. Because the Hamilton matrix in the expression has the properties of symplectic matrix, good stability is shown in the numerical calculation, so the precise integration method of two end boundary conditions can be adopted to realize the high-precision numerical solution of the system by means of computer programmers with Matlab. The simply method can be applied in the building structure with multi-lateral resistant elements composed of frame, shear wall, frame-supported shear wall, frame-tube, equivalent continuous tube and other lateral resistant elements. At the same time, the cases of variable cross-section along height of structure can be disposed easily. The frame-shear wall and frame-tube structural system were discussed as examples in the paper, concluding that results can be satisfied with accuracy requirement of preliminary design by comparison the results in present literature.The parallel Timoshenko beams adopted in this paper is a universal model which can be used for many kinds of high-rise building structure system. In addition, the Hamilton dual systems was introduced to obtain the state space equations,so the analogy between modern control-theory and building structure analysis was founded, which has laid a theoretical foundation for the mechanical analysis of building structure by using research fruits of modern control-theory for reference. The precise integration method together with Matlab computer language simplify calculations and improve calculating precision. This paper offers a universal model,a simply deduction and an effective calculation method,which will be more convenient in the process of preliminary design.